I. Field
The present invention relates generally to telecommunications, and more specifically to techniques for channel estimation in a communication system.
II. Background
In a typical telecommunications system, the data to be transmitted is encoded with a coder, such as, for example, a turbo coder, which generates a sequence of symbols, referred to as “code symbols.” Several code symbols may be blocked together and mapped to a point on a signal constellation, thereby generating a sequence of complex “modulation symbols.” This sequence may be applied to a modulator, which generates a continuous time signal, which is transmitted over a wireless channel.
At the receiver, the demodulator generates a sequence of modulation symbols or soft decisions. If soft decisions are generated, each soft decision represents an estimate of a modulation symbol that was transmitted over the channel. The estimates may be used to compute the log-likelihood ratio (LLR) of the code symbols. In the case of turbo coding, the turbo decoder uses the sequence of code symbol LLRs in order to decode the data that was originally transmitted.
When computing the LLRs of the code symbols, the propagation conditions of the channel should be considered. The channel conditions, or the channel impulse response, may be estimated at the receiver from a known pilot sequence embedded in the data transmission. By way of example, in Orthogonal Frequency Division Multiplexing (OFDM) systems, a Least Squares procedure is often used to estimate the channel. Using this procedure, the channel may be estimated from a set of pilot tones uniformly spaced across the frequency band of one OFDM symbol.
However, this channel estimate will be noisy because the pilot tones are corrupted with noise. Typically, in order to suppress the noise in the channel estimate for OFDM demodulation, the receiver typically averages (i.e. “filters”) the channel estimate from multiple OFDM symbols. In other words, the channel estimate is time-averaged across OFDM symbols.
When the channel estimate is time-averaged, the noise in the channel estimate is suppressed. In other words, the noise variance of the time-averaged channel estimate is smaller than that of the channel estimate without time-averaging. The longer the time-averaging window, the more the noise suppression. However, the time-averaged channel estimate, even without its noise component, may not be the same as the true channel in the presence of channel variation. This difference is called the channel estimation bias. Hence, the channel estimation error includes of the noise and the bias.
E.g., if actual channel variation occurs on a timeframe of about the duration of one OFDM symbol and a time-averaging window is about the duration of 10 OFDM symbols, then the channel estimation will not be accurate for the channel even without the noise.
E.g., if the actual channel does not vary for about the duration of 10 OFDM symbols and the time averaging window is about the duration of 4 OFDM symbols, then the channel estimation bias is zero.
Hence, the longer time-averaging window leads to smaller noise variance, but larger channel estimation bias. The shorter time-averaging window leads to smaller channel estimation bias, but larger noise variance.
Thus, there are two competing goals: (1) The time-averaging window should be long enough to sufficiently suppress the noise, but (2) the time-averaging window should be short relative to the actual channel variation timeframe to avoid excessive channel estimation bias. The problem is how to select an optimum or useful time-averaging window in light of the competing goals.
The optimal degree of averaging depends on the SNR and the channel Doppler, both of which are unknown a priori.
When operating in the low SNR regime, longer time averaging reduces noise variance at the expense of increasing estimation bias due to channel variation over the averaging window. Since noise is the dominant source of degradation at low SNR, it is better to have long time averaging in this case.
If the noise variance is small compared to the channel estimation bias, it may be preferable to shorten the averaging duration thereby reducing bias in the channel estimate.
The optimal degree of averaging depends on the channel Doppler and SNR. Ideally we desire a receiver that automatically varies the degree of time averaging, in order to obtain the least overall degradation across all channel conditions.
There are several adaptive channel estimation algorithms. See, for example, “Adaptive channel estimation with velocity estimator for W-CDMA receiver,” in Proc. IEEE VTC, May 2000, pp. 2024-2028, which is incorporated herein by reference. Typically, these algorithms estimate the access terminal speed and choose the amount of time-averaging based on a mathematical model for the fading statistics.
A common mathematical model for the fading statistics is Jakes' fading process. However, the many simplifying assumptions behind this model may not necessarily apply in the “real world”. Estimating access terminal speed and choosing the amount of time-averaging based on a highly-simplified mathematical model may result in significantly inaccurate estimates of the actual rate of channel variation. For example, the access terminal could determine that the channel is varying much faster than it is in reality, and hence it may use a much smaller degree of time-averaging than necessary. Conversely, the access terminal could determine that the channel is varying much slower than it is in reality, and hence it may use a much larger degree of time-averaging than is desirable. In either situation, the discrepancy can produce higher channel estimation error, leading to higher decoding error rates. This undesirable property is sometimes referred to as “model mismatch” or “model sensitivity”.